"That very well could lead to a government shutdown," Kennedy said, adding that a shutdown "would be stupid," according to CNN.

Funding for several agencies is set to lapse on Dec. 7.

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Senate Democrats have said they will push a spending bill to include language that protects Mueller from being fired without just cause if Republican leadership refuses to schedule the protection bill for a stand-alone floor vote.

Whitaker, who now oversees Mueller's probe, has expressed doubt about the necessity of the special counsel's investigation into Russian interference in the 2016 election, writing in an op-ed for CNN last year that the probe had "gone too far."